Venn Diagrams
๐ Log in to trackTwo question families: (1) region arithmetic โ count union, intersection, only-regions, exactly-two, neither using inclusion-exclusion over labelled Venn regions; (2) relation selection โ decide whether categories nest (definitional necessity), stay apart (impossibility) or intersect (possible but not forced). The arithmetic family is pure formula discipline; the relation family is two quick tests per pair. Label every region before computing and both become near-90% accuracy topics.
One page per subtopic: detailed notes, every question type, formulas, tricks and practice sets.
Every formula on one printable page, grouped by subtopic.
4 exam-level questions worked step by step.
55 questions โ untimed practice or a timed test with analysis.
Track record in the exam
Questions per shift in recent SSC CGL papers.
Test difficulty mix (55 questions)
Question patterns exams keep repeating
Taken from previous-year papers. If a pattern is marked "very common", expect to see it in your exam.
Two-set region count
very commonTwo totals and the overlap; asks at least one, only one or neither.
How to solve: Union = A + B โ both; neither = total โ union; only A = A โ both.
Example: In a class of 60, 35 like tea, 30 like coffee and 10 like both. How many like neither?
35 + 30 โ 10 = 55; 60 โ 55 = 5.
Reverse two-set puzzle
commonSome regions are given; the overlap, a circle total or the group size is asked.
How to solve: Draw four boxes (only A, only B, both, neither), fill the known ones and solve for the gap.
Example: Everyone in a class of 80 plays chess or carrom; 50 play chess and 40 carrom. How many play both?
50 + 40 โ 80 = 10.
Percentage-based sets
commonData in percent, answer in percent or in people.
How to solve: Solve in percent with total 100, convert to people at the end.
Example: 70% watch cricket, 60% football, 40% both. What percent watch neither?
Union 90% โ neither 10%.
Maximum / minimum overlap
occasionalOverlap not given; asks its largest or smallest possible value.
How to solve: Max both = smaller set; min both = A + B โ N (not below 0); max neither = N โ larger set.
Example: 80 people; 50 like cricket, 40 hockey. Maximum who like neither?
Hockey inside cricket โ neither = 80 โ 50 = 30.
Three-set union / none
very commonThree totals, three pairs, the triple and a group size.
How to solve: Union = ฮฃA โ ฮฃpairs + triple; none = total โ union.
Example: 200 people: coffee 90, tea 80, milk 70; pairs 40, 35, 30; all three 15. How many drink none?
Union 150 โ none 50.
Exactly two / exactly one
commonAsks for exactly one, exactly two or at least two sets.
How to solve: Exactly two = ฮฃpairs โ 3 ร triple; at least two = ฮฃpairs โ 2 ร triple; exactly one = union โ exactly two โ triple.
Example: Pairs 8, 7, 6 and all three 3. Exactly two?
21 โ 9 = 12.
Reading a region diagram
commonNumbers are written in each region; the question describes a group in words.
How to solve: List the regions the phrase covers and add them once each; use total โ regions for 'not' phrases.
Example: Only N 20, only T 25, only R 5, N-T 15, T-R 6, N-R 4, all 10. How many use exactly one source?
20 + 25 + 5 = 50.
Choose-the-diagram
very commonThree words; options describe circle pictures.
How to solve: For each pair decide inside / apart / cross by definition, then match all three marks to one picture.
Example: Even numbers, Odd numbers, Prime numbers.
Even and odd never meet; 2 and 3 are prime โ two separate circles, with the third intersecting both.